where we separated the dimensionless kernel, \(w(\xi ,\xi ^{\prime })\) , and the
factor, \(\Theta _{GR}\) , which is written for the case of the deformation interaction of carriers with the in-plane acoustic modes, see Refs. 10 and 15. Here \(D\)  is the deformation potential, \(s\)  is the sound velocity,
and \(\rho _s\)  is the sheet density of graphene. At room temperature and typical other parameters [1]} we obtain
\(\upsilon _{ac}\simeq 0.96\times 10^6\)  cm/s and \(\Theta _{GR}\simeq 5.06\times 10^{19}\) 
cm\(^{-2}\) s\(^{-1}\)  (notice, that \(\upsilon _{ac}\propto D^2\)  and we used \(D\simeq \)  12 eV).
The dimensionless kernel is plotted in Fig. 3 and the probability \(W(\varepsilon ,\varepsilon ^{\prime })\)  is suppressed fast if \((\varepsilon -\varepsilon ^{\prime })/T\ge \) 0.15. This cut-off factor is determined by the weak
ratio \(s/\upsilon \simeq \) 1/137 mainly while parameter \(g\)  determines a peak value
of \(W(\varepsilon ,\varepsilon ^{\prime })\) , c.f. Figs. 3a and 3b.
